Figure 4: Variation along the bond edge of the function F in the case k = 1 and with periodic boundary conditions. In Fig. 4 results are presented for k = 1 for cases where the boundary conditions along the plate edges parallel to the x1-axis are changed from being free to being periodic in order to study the interaction effects resulting from closely spaced bonds. By comparison of Figs. 3 and 4 the interaction of bonds reduces the strength more than the effect of free edges. It is emphasised that the present procedure for calculating bond strength assumes that the radius of curvature of the crack front and the distance from the crack front to the plate edges must be large compared to the plate thickness. Also effects of large-scale plastic deformation and crack face contact have not been included in the analysis. CONCLUSION Significant effects of edges on the strength of finite bonds within plates have been demonstrated by numerical examples. The stresses along the crack front are enhanced due to the presence of the plate edge. There is a tendency for periodic boundary conditions to raise the stress levels more than free boundaries. Especially the shear stresses are increased due to periodic boundary conditions, and dependent on the factor k in the fracture criterion (3), this will affect the strength of the bonds significantly. Calculations carried out for k = 2 , not shown here, indicate a larger decrease in bond strength due to periodic boundary conditions than the results for k = 1 (compare Figs. 3 and 4). Results for crack propagation following crack initiation under quasi-static conditions have been obtained in [1] based on a crack growth criterion. This issue has not been dealt with in the present work. It was shown in [1], however, that the ultimate strength of the bond might be significantly higher than initial strength where crack growth is initiated. Such effects could also be expected to play a role for the present problems. ACKNOWLEDGEMENTS – Support from the the EFP-2001 research programme on scale effects in design with composites is gratefully acknowledged.
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